This paper considers optimization of drug administration as a problem in the optimal control of a compartmental system. An optimal control is considered to be achieved when the concentration of drug in the plasma is maintained as planned for therapeutic effects, while the total dosage of drug is minimally sustained to reduce side effects. Two types of constraints are adopted: to maintain the concentration above the minimal effective level, and to maintain the mean concentration above a certain level. First we consider the problem in a general framework; we consider an nth order nonoscillatory linear compartmental system with a single input and a single constraint. Then we derive a theorem which gives an explicit formula of optimal input functions for the constraints considered. Finally a linear 2-compartment system is employed as a model for pharmacokinetics, and oral administration of drug is regarded as an impulsive input to the system. The previous theorem is applied to this problem, and then some properties of optimal drug administration are obtained. we also evaluate the conventional mode of drug administration in clinics in view of the results theoretically obtained.
ASJC Scopus subject areas
- Statistics and Probability
- Modeling and Simulation
- General Biochemistry, Genetics and Molecular Biology
- General Immunology and Microbiology
- General Agricultural and Biological Sciences
- Applied Mathematics